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IEEE International Symposium on Information Theory (ISIT)

Improved min-sum decoding algorithms for irregular LDPC codes

Jinghu Chen, R. Michael Tanner, C. Jones, Yan Li

Published Jan 1, 2005• 86 citations
Publisher

Abstract

In this paper, we apply two improved min-sum algorithms, the normalized and offset min-sum algorithms, to the decoding of irregular LDPC codes. We show that the behavior of the two algorithms in decoding irregular LDPC codes is different from that in decoding regular LDPC codes, due to the existence of bit nodes of degree two. We analyze and give explanations to the difference, and propose approaches to improve the performance of the two algorithms.

DOI
10.1109/isit.2005.1523374

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In this paper, we apply two improved min-sum algorithms, the normalized and offset min-sum algorithms, to the decoding of irregular LDPC codes. We show that the behavior of the two algorithms in decoding irregular LDPC codes is different from that in decoding regular LDPC codes, due to the existence of bit nodes of degree two. We analyze and give explanations to the difference, and propose approaches to improve the performance of the two algorithms.
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In this paper a modified Offset Min-Sum decoding algorithm for Low-Density Parity Check Codes is presented. In this modified algorithm, the offset factor in the original Offset Min-Sum algorithm is adjusted iteratively with the assistance of the check-node computation outputs of the Normalized Min-Sum algorithm. As a result, the offset factor in our modified algorithm can be calculated adaptively and more efficiently according to the previous decoding procedure, which can minimize the decoding degradation compared with the Belief Propagation decoding algorithm. The simulation results show that, compared with the original Offset Min-Sum decoding algorithm, our modified algorithm can achieve noticeable performance improvement with minor extra hardware complexity. For example, when BER is 10−5, our algorithm can achieve 0.1dB and 0.2dB decoding gain over Offset Min-Sum algorithm for regular and irregular LDPC codes respectively.
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This brief examines different parity-check node decoding algorithms for low-density parity-check (LDPC) codes, seeking to recoup the performance loss incurred by the min-sum approximation compared to sum-product decoding. Two degree-matched check node decoding approximations that depend on the check node degree dcare presented. Both have low complexity and can be applied to any degree distribution. Simulation results show near sum-product decoding performance for both degree-matched check node approximations for regular and irregular LDPCs
This paper presents a low complexity Min-Sum algorithm for decoding irregular Low-Density Parity-Check (LDPC) codes. In the proposed algorithm, the significant improvement in the error correcting performance without enhancing the hardware complexity is achieved by employing adaptive and optimized normalization factors for both the extrinsic information and log-likelihood ratio data bits respectively. The experimental results demonstrate that the proposed algorithm with 6-bit non-uniform quantization achieves reasonable decoding performance in terms of Frame Error Rate (FER) and Bit Error Rate (BER) without increasing the hardware complexity by avoiding finite word length effects of soft information.